A Riemannian rank-adaptive method for low-rank optimization

This paper presents an algorithm that solves optimization problems on a matrix manifold M⊆Rm×n with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. Th...

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) 2016-06, Vol.192, p.72-80
Main Authors: Zhou, Guifang, Huang, Wen, Gallivan, Kyle A., Van Dooren, Paul, Absil, Pierre-Antoine
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convergence
Efficiency
Fixed-rank manifold
Inequalities
Low-rank approximation
Low-rank optimization
Manifolds
Mathematical analysis
Optimization
Rank-constrained optimization
Riemannian manifold
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Summary:This paper presents an algorithm that solves optimization problems on a matrix manifold M⊆Rm×n with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted low-rank approximation problem is used to illustrate the efficiency and effectiveness of the algorithm.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2016.02.030